Samantha and Isaac are playing racquetball samantha hits the ball sending it onto a trajectory modeled by y= -3 |x-4|+20 where y is the height reached by the ball in feet after x milliseconds in a desperate attempt to keep the ball in the air Issac throws his racquet toward it at a trajectory modeled by y=1/3x+4 when does his racquet hit the ball
To find when Isaac's racquet hits the ball, we need to find the point of intersection between the two trajectories.
Setting y equal to each other, we get:
-3|x-4| + 20 = 1/3x + 4
We can split this equation into two cases:
Case 1: x < 4
-3(4-x) + 20 = 1/3x + 4
-12 + 3x + 20 = 1/3x + 4
3x + 8 = 1/3x + 4
9x + 24 = x + 12
8x = -12
x = -1.5
Case 2: x >= 4
-3(x-4) + 20 = 1/3x + 4
-3x + 12 + 20 = 1/3x + 4
-3x + 32 = 1/3x + 4
-9x + 96 = x + 12
-10x = -84
x = 8.4
Therefore, Isaac's racquet will hit the ball at x = 8.4 milliseconds.